9. Linear Transformations

Finding Matrices Of Transformations — Quiz

Test your understanding of finding matrices of transformations with 5 practice questions.

Practice Questions

Question 1

A linear transformation $T$ from $\mathbb{R}^2$ to $\mathbb{R}^2$ satisfies $T(\mathbf e_1)=\begin{bmatrix}2\\1\end{bmatrix}$ and $T(\mathbf e_2)=\begin{bmatrix}-1\\3\end{bmatrix}$. What is the matrix of $T$?

Question 2

The transformation $T$ is defined by $T(x,y)=(4x,2y)$. What is the matrix of $T$?

Question 3

What is the matrix of the reflection across the $x$-axis in $\mathbb{R}^2$?

Question 4

What is the matrix of the projection onto the $x$-axis in $\mathbb{R}^2$?

Question 5

What is the matrix of a $90^\circ$ counterclockwise rotation in $\mathbb{R}^2$?